Paper :

Spectral link of the generalized Townsend-Perry constants in turbulent boundary layers Björn Birnir, Luiza Angheluta, John Kaminsky, and Xi Chen Phys. Rev. Research 3, 043054 – Published 21 October 2021

https://journals.aps.org/prresearch/abstract/10.1103/PhysRev...

https://arxiv.org/abs/2006.13445

> The formulas describe the complex behavior of a liquid when it meets a boundary

Since Reynolds (1842–1912) proposed Reynolds averaging, there have been numerical approximations for turbulent flow. This paper proposes one more, perhaps better, such approximation for turbulent flow near a wall.

SciAm is totally blowing this out of proportion with their title.

If someone proposed yet another heuristic solution algorithm to the Travelling Salesman Problem, you shouldn't write an article "NP-hard problems finally solved after 50 years".

This is Scientific American blowing a paper’s significance way out of proportion.

A pretty specific kind of turbulence modeling has been improved, this is not some grand general analytic theory of turbulence.

Scientific American should be ignored unless and until they fix the editorial problems that led to their pathetic attack on Edward O Wilson. Scott Aaronson's blog had a good writeup; HN discussion here: https://news.ycombinator.com/item?id=29778348

As a layman who is interested in the field but knows little about the current state: is this related to or advancing our knowledge towards a generalized solution of the Navier-Stokes equations?

As far as I can tell, this paper has nothing to do the generalized solution to the Navier-Stokes equations. It deals with flows near surfaces (boundary layers) and not flows in general. After skimming the paper I could only find one mention of the Navier-Stokes equations, and that was just for a channel flow identity derived from the Navier-Stokes equations under very particular boundary conditions (so not general at all).

This paper provides an interesting connection between the spectral properties of turbulence and the second-order moments of velocity in boundary layers (the "spectral link" as the title says). That is interesting to experts but it is a bit too abstract for the general public to understand easily, unfortunately.

No. This is a better approximation for boundary layer turbulence, it's not a golden equation. Better approximations for annoying problems in fluid dynamics are published quite often. I think has plenty of practical use though, I'll probably be trying to integrate it into some cfd work to see how it behaves compared to our current approach at work. Disclaimer that I am not a physics phd, but I do work with a hydraulic research group so I've picked up bits and pieces.

If you want to see a fun example of fluid dynamics approximations, look at the Wikipedia pages for the Darcy friction factor and Colebrook white equation.

I would also like to know that.

If this is as important as it seems, why is it taking so much time from publication for journals like Scientific American to pick up on it? The paper authors, Birnir et al, seem to have done a very good job of summarizing their results in a clear and succinct way for a review paper in a letters journal. Kudos to them.

They are popular journals, not scientific ones and fluid dynamics is apparently not sexy (though planes are — go figure!)

I’m pretty stoked by these results.

(Sorry about the pun)

Deep cut but I’ll allow it

It isn’t that important.

It is an incremental, but perhaps significant improvement for describing flow in a certain situation. It is nothing like a general purpose “solution” to turbulence.

Scientific American kind of sucks.

I mean, the certain situation is the exact problem where fusion reactors are most leaky. Decades of effort has been put into more efficiently computationally modeling plasma turbulence at the boundary.

Yeah Scientific American sucks ass but this is an important area of research and it's ripe for a (or many) breakthroughs.

It isn't that important, the website just tries to make it seem that way. It's useful, but there were already models to estimate boundary layer turbulence. This is just a better approximation.

Amd why are there still only 7 comments on this? Wasn't this one of the major unsolved problems of physics? If they had used a recurrent learning model to figure it out people would care...

Sciam is dealing with a lot of race and gender issues right now, so topics like this are on hold.

I’m not a native speaker, so this might be a dumb question. So far, I always associated word “discover” with “something is there, someone just managed to stumble upon it while wondering around”. Thus, I find the word’s use quite strange when it comes to scientific work, especially equations —- the authors probably didn’t wonder around and invested quite a lot of work to come up with the equation.

Does it make sense to say “someone discovered an equation for X”? If not, what would be a better word?

I don't think discover implies anything about the effort put in on its own. If anything I'd say it leans towards deliberate effort, even if not always an expected result.

If it's just a fluke then more often and not I'd expect to see that spelled out as either context, or with the words you used: "stumbled upon".

At any rate, I think the reason it's used in this context in particular is because it represents that the 'equation' is not just a mathematical construct someone came up with, but that it represents observable reality in a way that is novel and perhaps unexpected. It wasn't something someone made up, it's something that usefully describes phenomena that are outside human control. Thus, they did not invent, instead they discovered.

Whether equations are invented or discovered is actually a matter of philosophy... somewhere in the areas ontology and epistemology. And the debate is not really settled, I believe.

https://www.pbs.org/wgbh/nova/article/great-math-mystery/

As a native speaker discover sounds fine to me but you are likely looking for a word like derived or calculated.

When I did my engineering degree I got the impression that the "important" discoveries had already been made. I think this pushed me away from pursuing research (plus horror stories from academia) because it didn't seem very exciting. I wish I had understood how many holes there were still to be filled!

So, I think the title misleads. The discovery is regarding the boundary layer, not just turbulence. Im pretty sure my 25 year old fluid mechanics book has equations for turbulence, just none for the area between turbulent and laminar flows. Forgive me if I'm wrong, its been... well 25 years.

This is very exciting!